As stated above, ADR is used a lot in big productions.
Wireless body mics hidden in the actors' clothing are capable of capturing the actor's voice while picking up only a tiny bit of the background noise. They are typically highly directional and placed very close to the mouth, so the ratio of the voice level to the background level can be tremendous, making it easier to reduce or eliminate in post production. For wind in particular, physical wind screens (even on tiny lapel mics) and a little post-processing can go a long way to attenuating the volume.
I don't know if it's routinely used in film and TV production, but it's possible to "subtract" much of the background noise if you have multiple recordings of the same scene. For example, independent recordings of Dolores and Maeve's mics will contain nearly identical background noise but be very distinct when one or the other is speaking. Digital signal processing can recognize the commonality those recordings to essentially reconstruct the background noise isolated from the voice audio. That reconstructed noise can then be subtracted out. (The old Nexus One phone had a back-facing microphone to capture ambient noise that was subtracted from the audio captured by the front in order to provide a clearer audio signal.)
When the Today show folks go out into the plaza, it's done live (maybe with a small delay). There's no chance for ADR. If you've ever been there in person, you know the crowd noise can be tremendous. Standing 15-20 feet from the presenters, you cannot hear them (at all!) over the din of crowd. Yet their mics register the crowd noise at far lower levels than that of the presenters' voices. The noise is so low, in fact, that the sound engineers have extra microphones to capture the ambient sound so they can mix the crowd noise back in to make the broadcast audio feel realistic.